Linear Regression

Implements a Python executable file called linear_regression.py that uses linear regression to fit a polynomial function to the data.

Arguments

1. The first argument, <training_file>, is the path name of the training file, where the training data is stored. The path name can specify any file stored on the local computer.

2. The second argument, <degree> is an integer between ₁ and ₁0. We will not test your code with any other values. The degree specifies what function φ you should use.

Suppose that you have an input vector x = (x₁, x₂, ..., x_D)^T

• If the degree is 1, then φ(x) = (1, x₁, x₂, ..., x_D)^T.
• If the degree is 2, then φ(x) = (1, x₁, (x₁)², x₂, (x₂)²..., x_D, (x_D)²)^T.
• If the degree is 3, then φ(x) = (1, x₁, (x₁)², (x₁)³, x₂, (x₂)², (x₂)³, ..., x_D, (x_D)², (x_D)³)^T.

3. The third argument, <λ>, is a non-negative real number (it can be zero or greater than zero). This is the value of λ that you should use for regularization. If λ = 0, then no regularization is used.

4. The fourth argument, <test_file>, is the path name of the test file, where the test data is stored. The path name can specify any file stored on the local computer.

Test Cases

• Degree = 1 and λ = 0
• Degree = 1 and λ = 1
• Degree = 2 and λ = 0
• Degree = 2 and λ = 1